authorea.com/62406

Chirp manipulation

Zero centered baseband chirp:

\[s(t) = e^{j\pi\gamma t^2}\] where \(t\) - time; \(\gamma = \frac{B}{\tau}\) - frequency slope; \(B\) - chirp bandwidth; \(\tau\) - chirp duration; \(T\) - sampling period; \(2M\) - number of samples.

```
M = 100;
n = -M : M-1;
T = 0.1;
t = n*T;
gamma = 0.15;
sChirp = exp(1j*pi*gamma*t.^2);
plot_complex(t, sChirp, 'time')
```

\[S(f) = \mathcal{F}(s(t)) = \int_{-\infty}^{\infty } {e^{j\pi\gamma t^2} e^{-j2\pi f t}dt}\]

```
SChirp = fft(sChirp);
f = (0:2*M-1)/(T*2*M);
plot_complex(f, SChirp, 'freq')
```

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